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we can say that a tautology is a formula which is always true for every value of its proportional variables; it means it contains T in the final conclusion of its truth table.
The tautology of a given statement can be found by making the truth table . If the value in the last column is true then the statement is tautology and if the values in the last column is false then the statement is not tautology. For example :- either raj will go to market or raj will not go market.
We will do some examples or a truth table to check that the given statement is tautology or not.
WHAT IS TAUTOLOGY?
A compound statement which is always true regardless of value assigned to its component proposition is called tautology.
Or we can say that a tautology is a formula which is always true for every value of its proportional variables; it means it contains T in the final conclusion of its truth table.
In maths tautology means the logical compound which gives results in a true statement.
For example :- 1. She is healthy or she is not healthy.
- Seema is a good girl or seema is not a good girl.
USE TRUTH TABLE TO DETERMINE WHETHER THE GIVEN STATEMENT IS TAUTOLOGY
- p v ~ p
p | ~ p | p v ~ p |
T | F | T |
F | T | T |
- qv [~ (q∧ r) ∧ ~ q]
p r | ~ q | (q∧ r) | ~ (q∧ r) | ~ (q∧ r)∧ ~ q | q ∨ [~ (q∧ r)∧ ~ q |
T T | F | T | F | F | T |
T F | F | F | T | F | T |
F T | T | F | T | T | T |
- (p∨ q)∨ (~ p∨ q)
p q | ~ p | (p∨ q) | (~ p∨ q) | (p∨ q)∨ (~ p∨ q) |
T T | F | T | T | T |
T F | F | T | F | T |
F T | T | T | T | T |
F F | T | F | T | T |
LOGIC SYMBOLS OF TAUTOLOGY
symbol | meaning | representation |
∧ | AND | A ∧ B |
∨ | OR | A ∨ B |
~ | NOT | ~A |
→ | IMPLIES | A→B |
⇔ | IF AND ONLY IF | A⇔B |
AND OPERATION
When two simple statement are used to for a compound statement .It is denoted by ‘ ∧‘.
Let X and Y be two statement :
X | Y | X Y |
T | T | T |
T | F | F |
F | T | F |
F | F | F |
OR OPERATION
The compound statement is formed by the two simple statements using the OR symbol.
Symbol of OR operation is ‘∨ ’.
Let X and Y be two statement :
X | Y | X∨ Y |
T | T | T |
T | F | T |
F | T | T |
F | F | F |
NOT OPERATION
When that statement’s truth value changes using the word NOT .
It is denoted by ‘~ ’.
Let X and Y be two statement :
X | ~ X |
T | F |
F | T |
BI-CONDITIONAL OPERATION
The compound statement is formed by two simple statements using the phrase if and only if .
It is denoted by ‘⇔ ‘.
Let X and Y be two statement :
X | Y | X⇔ Y |
T | T | T |
T | F | F |
F | T | F |
F | F | T |
CONCLUSION
In this article we study tautology, meaning of tautology, and do some examples of tautology. It is an expression which says the same thing two times in different ways.
Tautology says that A compound statement which is always true regardless of value assigned to its component proposition is called tautology.
We also do different types of symbols used in tautology.
